Describing Transformations of Rational Functions

Let's start by recalling possible transformations of the parent function $f (x) = \frac{1}{x} .$

Function	Transformation of the Graph of $f (x) = \frac{1}{x}$
$g (x) = \frac{1}{x} + k$	Vertical translation by $k$ units. If $k > 0,$ the translation is up. If $k < 0,$ the translation is down.

Now, let's consider the given function. $g (x) = \frac{1}{x} - 7 \Leftrightarrow g (x) = \frac{1}{x} + (- 7)$ We can see that $k = - 7 .$ Therefore, the graph of $g (x)$ is a translation of the graph of $f (x)$ $7$ units down.

Describing Transformations of Rational Functions 1.10 - Solution